Topology of Real Unitary Space

Noboru Endou

Gifu National College of Technology

Takashi Mitsuishi

Miyagi University

Yasunari Shidama

Shinshu University, Nagano

Summary.

In this article we introduce three subjects in real unitary space: parallelism of subsets, orthogonality of subsets and topology of the space. In particular, to introduce the topology of real unitary space, we discuss the metric topology which is induced by the inner product in the space. As the result, we are able to discuss some topological subjects on real unitary space.

MML Identifier: RUSUB_5

Contents (PDF format)

1. Parallelism of Subspaces
2. Orthogonality
3. Topology of Real Unitary Space

Bibliography

[1] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Journal of Formalized Mathematics, 14, 2002.

[3] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Subspaces and cosets of subspace of real unitary space. Journal of Formalized Mathematics, 14, 2002.

[4] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

[5] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[6] Jan Popiolek. Introduction to Banach and Hilbert spaces --- part I. Journal of Formalized Mathematics, 3, 1991.

[7] Jan Popiolek. Introduction to Banach and Hilbert spaces --- part II. Journal of Formalized Mathematics, 3, 1991.

[8] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[9] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.

[10] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.

[11] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.

[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.